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Wikispaces>genewardsmith **Imported revision 146041359 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 146122899 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-31 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-31 21:56:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>146122899</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) | 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) | ||
19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents) | 19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents) | ||
==5-limit commas== | |||
135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 cents) | |||
648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents) | |||
16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents) | |||
250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents) | |||
128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents) | |||
3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents) | |||
20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents) | |||
81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents) | |||
2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents) | |||
67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents) | |||
78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents) | |||
393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents) | |||
15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents) | |||
</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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70368744177664 / 68630377364883 = |46 -29&gt;: 29-comma (43.305 cents)<br /> | 70368744177664 / 68630377364883 = |46 -29&gt;: 29-comma (43.305 cents)<br /> | ||
36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br /> | 36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br /> | ||
19383245667680019896796723 / 19342813113834066795298816 = |-84 53&gt;: Mercator's comma, 53-comma (3.615 cents)</body></html></pre></div> | 19383245667680019896796723 / 19342813113834066795298816 = |-84 53&gt;: Mercator's comma, 53-comma (3.615 cents)<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit commas</h2> | |||
<br /> | |||
135 / 128 = |-7 3 1&gt;: major chroma, major limma, pelogic comma (92.179 cents)<br /> | |||
648 / 625 = |3 4 -4&gt;: major diesis, diminished comma (62.565 cents)<br /> | |||
16875 / 16384 = |-14 3 4&gt;: negri comma, double augmentation diesis (51.120 cents)<br /> | |||
250 / 243 = |1 -5 3&gt;: maximal diesis, porcupine comma (49.166 cents)<br /> | |||
128 / 125 = |7 0 -3&gt;: diesis, augmented comma (41.059 cents)<br /> | |||
3125 / 3072 = |-10 -1 5&gt; small diesis, magic comma (29.614 cents)<br /> | |||
20000 / 19683 = |5 -9 4&gt;: minimal diesis, tetracot comma (27.660 cents)<br /> | |||
81 / 80 = |-4 4 -1&gt;: syntonic comma, Didymos comma, meantone comma (21.506 cents)<br /> | |||
2048 / 2025 = |11 -4 -2&gt;: diaschisma (19.553 cents)<br /> | |||
67108864 / 66430125 = |26 -12 -3&gt;: misty comma (17.599 cents)<br /> | |||
78732 / 78125 = |2 9 -7&gt;: medium semicomma, sensipent comma (13.399 cents)<br /> | |||
393216 / 390625 = |17 1 -8&gt;: Wuerschmidt comma (11.445 cents)<br /> | |||
15625 / 15552 = |-6 -5 6&gt;: kleisma, semicomma majeur (8.107 cents)</body></html></pre></div> | |||
Revision as of 21:56, 31 May 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-05-31 21:56:26 UTC.
- The original revision id was 146122899.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
A **comma** is a small just interval, greater than 1 and not a power such as a square or cube of any other interval, generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is //tempered out//, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by [[Meantone|meantone temperament]]. ==3-limit commas== 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 cents) 2187 / 2048 = |-11 7>: apotome (113.685 cents) 531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents) 134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents) 70368744177664 / 68630377364883 = |46 -29>: 29-comma (43.305 cents) 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) 19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents) ==5-limit commas== 135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 cents) 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents) 16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents) 250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents) 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents) 3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents) 20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents) 81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents) 2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents) 67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents) 78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents) 393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents) 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)
Original HTML content:
<html><head><title>Comma</title></head><body>A <strong>comma</strong> is a small just interval, greater than 1 and not a power such as a square or cube of any other interval, generally in a <a class="wiki_link" href="/Harmonic%20Limit">low prime limit</a>. The word is often used in reference to <a class="wiki_link" href="/Regular%20Temperaments">regular tempering</a> when the comma is <em>tempered out</em>, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by <a class="wiki_link" href="/Meantone">meantone temperament</a>. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->3-limit commas</h2> <br /> 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 cents)<br /> 2187 / 2048 = |-11 7>: apotome (113.685 cents)<br /> 531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents)<br /> 134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents)<br /> 70368744177664 / 68630377364883 = |46 -29>: 29-comma (43.305 cents)<br /> 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents)<br /> 19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit commas</h2> <br /> 135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 cents)<br /> 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents)<br /> 16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents)<br /> 250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents)<br /> 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents)<br /> 3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents)<br /> 20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents)<br /> 81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents)<br /> 2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents)<br /> 67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents)<br /> 78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents)<br /> 393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents)<br /> 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)</body></html>